Low Data Complexity Research Articles

Improving Machine Learning Predictive Capacity for Supply Chain Optimization through Domain Adversarial Neural Networks

In today’s dynamic business environment, the accurate prediction of sales orders plays a critical role in optimizing Supply Chain Management (SCM) and enhancing operational efficiency. In a rapidly changing, Fast-Moving Consumer Goods (FMCG) business, it is essential to analyze the sales of the products and accordingly plan the supply. Due to low data volume and complexity, traditional forecasting methods struggle to capture intricate patterns. Domain Adversarial Neural Networks (DANNs) offer a promising solution by integrating transfer learning techniques to improve prediction accuracy across diverse datasets. This study presents a new sales order prediction framework that combines DANN-based feature extraction and various machine learning models. The DANN method generalizes the data, maintaining the data behavior’s originality. The approach addresses challenges like limited data availability and high variability in sales behavior. Using the transfer learning approach, the DANN model is trained on the training data, and this pre-trained DANN model extracts relevant features from unknown products. In contrast, Machine Learning (ML) algorithms are used to build predictive models based on it. The hyperparameter tuning of ensemble models such as Decision Tree (DT) and Random Forest (RF) is also performed. Models like the DT and RF Regressor perform better than Linear Regression and Support Vector Regressor. Notably, even without hyperparameter tuning, the Extreme Gradient Boost (XGBoost) Regressor model outperforms all the other models. This comprehensive analysis highlights the comparative benefits of various models and establishes the superiority of XGBoost in predicting sales orders effectively.

Cryptanalysis of QARMAv2

QARMAv2 is a general-purpose and hardware-oriented family of lightweight tweakable block ciphers (TBCs) introduced in ToSC 2023. QARMAv2, as a redesign of QARMAv1 with a longer tweak and tighter security margins, is also designed to be suitable for cryptographic memory protection and control flow integrity. The designers of QARMAv2 provided a relatively comprehensive security analysis in the design specification, e.g., some bounds for the number of attacked rounds in differential and boomerang analysis, together with some concrete impossible differential, zerocorrelation, and integral distinguishers. As one of the first third-party cryptanalysis of QARMAv2, Hadipour et al., [HGSE24] significantly improved the integral distinguishers of QARMAv2, and provided the longest concrete distinguishers of QARMAv2 up to now. However, they provided no key recovery attack based on their distinguishers. This paper delves into the cryptanalysis of QARMAv2 to enhance our understanding of its security. Given that the integral distinguishers of QARMAv2 are the longest concrete distinguishers for this cipher so far, we focus on integral attack. To this end, we first further improve the automatic tool introduced by Hadipour et al. [HSE23,HGSE24] for finding integral distinguishers of TBCs following the TWEAKEY framework. This new tool exploits the MixColumns property of QARMAv2 to find integral distinguishers more suitable for key recovery attacks. Then, we combine several techniques for integral key recovery attacks, e.g., Meet-in-the-middle and partial-sum techniques to build a fine-grained integral key recovery attack on QARMAv2. Notably, we demonstrate how to leverage the low data complexity of the integral distinguishers of QARMAv2 to reduce the memory complexity of the meet-in-the-middle technique. As a result, we successfully present the first concrete key recovery attacks on reduced-round versions of QARMAv2. This includes attacking 13 rounds of QARMAv2-64-128 with a single tweak block (T = 1), 14 rounds of QARMAv2-64-128 with two independent tweak blocks (T = 2), and 16 rounds of QARMAv2-128-256 with two independent tweak blocks (T = 2), all in an unbalanced setting. Our attacks do not compromise the claimed security of QARMAv2, but they shed more light on the cryptanalysis of this cipher.

The reality of backdoored S-Boxes—An eye opener

The real-life incidents researched in academia have revealed that (possibly) state-level efforts are made to camouflage the intentional flaws in the mathematical layer of an S-Box for exploiting the information-theoretic properties, i.e., Kuznyechik. To investigate the common features in the intentionally weakened mappings, this research thoroughly examines the backdoored structures from the perspective of 24 cryptanalytic attack vectors available in the open literature. We have debunked the earlier claims by the backdoor engineers that the proposed designs are stealthy against statistical distinguishers. Although a backdoored architecture fulfils the notions of randomness, it lacks the strength to resist sophisticated cryptanalytic attacks. Our analysis has revealed that during the backdoor insertion phase, a malicious designer compromises vital cryptographic properties, prominently the algebraic degree, differential trails, avalanche characteristics and leaving the open ground for hybrid cryptanalytic attacks. It is also observed that these mappings attain the upper bound of BCT, FBCT and DLCT, paving the way for hybrid attacks with high probability and lower data complexity.

Improved Attacks on LowMC with Algebraic Techniques

The LowMC family of SPN block cipher proposed by Albrecht et al. was designed specifically for MPC-/FHE-/ZKP-friendly use cases. It is especially used as the underlying block cipher of PICNIC, one of the alternate third-round candidate digital signature algorithms for NIST post-quantum cryptography standardization. The security of PICNIC is highly related to the difficulty of recovering the secret key of LowMC from a given plaintext/ciphertext pair, which raises new challenges for security evaluation under extremely low data complexity.In this paper, we improve the attacks on LowMC under low data complexity, i.e. 1 or 2 chosen plaintext/ciphertext pairs. For the difference enumeration attack with 2 chosen plaintexts, we propose new algebraic methods to better exploit the nonlinear relation inside the introduced variables based on the attack framework proposed by Liu et al. at ASIACRYPT 2022. With this technique, we significantly extend the number of attack rounds for LowMC with partial nonlinear layers and improve the success probability from around 0.5 to over 0.9. The security margin of some instances can be reduced to only 3/4 rounds. For the key-recovery attack using a single plaintext, we adopt a different linearization strategy to reduce the huge memory consumption caused by the polynomial methods for solving multivariate equation systems. The memory complexity reduces drastically for all 5-/6-round LowMC instances with full nonlinear layers at the sacrifice of a small factor of time complexity. For 5-round LowMC instances with a block size of 129, the memory complexity decreases from 286.46 bits to 248.18 bits while the time complexity even slightly reduces. Our results indicate that the security for different instances of LowMC under extremely low data complexity still needs further exploration.

Improved mixture differential attacks on 6-round AES-like ciphers towards time and data complexities

AES is the most widely used symmetric cipher. Many cryptographic primitives are designed following the structure of AES, called AES-like ciphers. Mixture differential cryptanalysis is a structural cryptanalysis technique for AES, which gave the best key recovery attack on 5-round AES in the chosen-plaintext setting and attacks with practical data and memory complexities on round-reduced AES. In this paper, we study the mixture differential attacks on 6 rounds of AES-like ciphers, and propose two improved attacks towards optimizing time and data complexities respectively. As an application to AES, we give the improved mixture differential attack on 6 rounds of AES-128 with time complexity 262.74, reducing by a factor of 210.26 compared with the previous mixture differential attack. For low data complexity, we show the improved 6-round mixture differential attack on AES-128 with data complexity 224.05, reducing by a factor of about 4. We also apply two attacks to 6 super-rounds of Saturnin, one of the second-round candidates in NIST lightweight cryptography standardization process, which is the first security evaluation of Saturnin against mixture differential cryptanalysis.

Cryptanalyzing an image cipher using multiple chaos and DNA operations

Recently, an improved color image cipher (ICIC-DNA) based on multiple deoxyribonucleic acid (DNA) sequence operations with DNA synthetic image and chaos was proposed. ICIC-DNA features the use of multiple chaotic systems and diverse DNA operations. However, after our careful cryptanalysis, we found that ICIC-DNA has several fatal security flaws. First, despite the use of multiple chaotic systems, the corresponding encryption sequences are independent of the plaintext, such that equivalent keys exist. Second, the diverse DNA operation is essentially a 2-bit data substitution process, and thus can be equivalently simplified. Third, ICIC-DNA includes substitution and permutation of DNA domains, and based on the equivalent simplification operation, the substitution and permutation can be attacked separately. Based on these, we propose a chosen-plaintext attack method to attack ICIC-DNA. Differential analysis is firstly adopted to break the DNA-base permutation process, and then the DNA domain encryption is eliminated, and finally the equivalent key is used to achieve complete cracking. Theoretical analysis and experimental results show that the proposed attack method is effective and has low computational complexity and data complexity.

New Results on Machine Learning-Based Distinguishers

Machine Learning (ML) is almost ubiquitously used in multiple disciplines nowadays. Recently, we have seen its usage in the realm of differential distinguishers for symmetric key ciphers. It has been shown that ML-based differential distinguishers can be easily extended to break round-reduced versions of ciphers. In this paper, we show new distinguishers on the unkeyed and round-reduced versions of SPECK-32, SPECK-128, ASCON, SIMECK-32, SIMECK-64, and SKINNY-128. We explore multiple avenues in the process. In summary, we use neural networks and support vector machines in various settings (such as varying the activation function), apart from experimenting with a number of input difference tuples. Among other results, we show a distinguisher of 8-round SPECK-32 that works with low data complexity.

Deep hybrid models for daily natural gas consumption forecasting and complexity measuring

AbstractAccurately forecasting daily natural gas consumption (NGC) is challenging due to its complex time‐varying high‐dimensional features. Therefore, this paper proposes a novel hybrid model for daily NGC forecasting consisting of two stages. In Phase I, the parallel local outlier factor‐isolation forest‐based data preprocessing algorithm is applied to denoise input data and preserve valuable features. In Phase II, the convolutional neural network (CNN)–stacked long short‐term memory (SLSTM) can extract and model spatio‐temporal features and is a hybrid deep learning forecaster. The influencing mechanism of different factors on the daily NGC prediction accuracy has not been mathematically and experimentally revealed. Thus, a hybrid complexity measure model () is developed by combining the variation coefficient analysis, local fluctuation coefficient analysis, and kurtosis analysis. The historical data sets of three representative cities were collected in the case studies, and six advanced models were selected for comparison. The results reveal that high‐quality input data preprocessed in Phase I enables better prediction performance for all models. The CNN‐SLSTM outperforms other algorithms with an average prediction improvement of about 26%–49%. Prediction models perform better in low NGC periods and cities with predominantly industrial natural gas users due to their lower data complexity.

Truncated Differential Attacks on Contracting Feistel Ciphers

We improve truncated differential attacks on t-branch contracting Feistel ciphers with a domain size of Nt. Based on new truncated differentials, a generic distinguisher for t2 + t − 2 rounds using O(Nt−1) data and time is obtained. In addition, we obtain a key-recovery attack on t2 + 1 rounds with Õ(Nt−2) data and Õ(Nt−1) time. Compared to previous results by Guo et al. (ToSC 2016), our attacks cover more rounds with a lower data-complexity. Applications of the generic truncated differential to concrete ciphers include full-round attacks on some instances of GMiMC-crf, and the best-known key-recovery attack on 17 rounds of the Chinese block cipher standard SM4. In addition, we propose an automated search method for truncated differentials using SMT, which is effective even for trails with probability below the probability of the truncated differential for a random permutation.

On Grain-Like Small State Stream Ciphers Against Fast Correlation Attacks: Cryptanalysis of Plantlet, Fruit-v2 and Fruit-80

Abstract The fast correlation attack (FCA) is one of the most important cryptanalytic techniques against LFSR-based stream ciphers. In CRYPTO 2018, Todo et al. found a new property for the FCA and proposed a novel algorithm which was successfully applied to the Grain family of stream ciphers. Nevertheless, these techniques cannot be directly applied to Grain-like small state stream ciphers with keyed update, such as Plantlet, Fruit-v2 and Fruit80. In this paper, we study the security of Grain-like small state stream ciphers by the FCA. We first observe that the number of required parity-check equations can be reduced when there are multiple different parity-check equations. With exploiting the Skellam distribution, we introduce a sufficient condition to identify the correct LFSR initial state and derive a new relationship between the number and bias of the required parity-check equations. Then, a modified algorithm is presented based on this new relationship, which can recover the LFSR initial state no matter what the round key bits are. Under the condition that the LFSR initial state is known, an algorithm is given against the degraded system and to recover the NFSR state at some time instant, along with the round key bits. As cases study, we apply our cryptanalytic techniques to Plantlet, Fruit-v2 and Fruit-80. As a result, for Plantlet, our attack takes $ 2^{73.75} $ time complexity and $ 2^{73.06} $ keystream bits to recover the full 80-bit key. Regarding Fruit-v2, $ 2^{55.34} $ time complexity and $ 2^{55.62} $ keystream bits are needed to determine the secret key. As for Fruit-80, $2^{64.47}$ time complexity and $2^{62.82}$ keystream bits are required to recover the secret key. More flexible attacks can be obtained with lower data complexity at the cost of increasing the attack time. Especially, for Fruit-v2, a key recovery attack can be launched with data complexity of $2^{42.38}$ and time complexity of $2^{73.31}$. Moreover, we have implemented our attack methods on a toy version of Fruit-v2. The attack matches the expected complexities predicted by our theoretical analysis quite well, which proves the validity of our cryptanalytic techniques.

Low-Data Cryptanalysis On SKINNY Block Cipher

Abstract At CRYPTO 2021, Dong et al. proposed an automatic method of Meet-in-the-Middle (MITM) key-recovery attacks. In this paper, we further extend it to a new automatic model which can be used to find low-data complexity attacks. With the help of the automatic model, we propose MITM attacks against reduced-round versions of all the six members of the SKINNY family with extremely low-data complexity. More precisely, we present MITM attacks against 19-round SKINNY-$n$-$3n$, 15-round SKINNY-$n$-$2n$, 11-round SKINNY-$n$-$n$ with three, two, one plaintext-ciphertext pairs, separately. In addition, we can attack two more rounds and three more rounds with no more than $2^8$ and $2^{32}$ data complexity, respectively.

A Data Efficient and Feasible Level Set Method for Stochastic Convex Optimization with Expectation Constraints

Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer to as algorithmic data complexity. Recent stochastic first order methods exhibit low data complexity when handling SOECs but guarantee near-feasibility and near-optimality only at convergence. These methods may thus return highly infeasible solutions when heuristically terminated, as is often the case, due to theoretical convergence criteria being highly conservative. This issue limits the use of first order methods in several applications where the SOEC constraints encode implementation requirements. We design a stochastic feasible level set method (SFLS) for SOECs that has low data complexity and emphasizes feasibility before convergence. Specifically, our level-set method solves a root-finding problem by calling a novel first order oracle that computes a stochastic upper bound on the level-set function by extending mirror descent and online validation techniques. We establish that SFLS maintains a high-probability feasible solution at each root-finding iteration and exhibits favorable iteration complexity compared to state-of-the-art deterministic feasible level set and stochastic subgradient methods. Numerical experiments on three diverse applications validate the low data complexity of SFLS relative to the former approach and highlight how SFLS finds feasible solutions with small optimality gaps significantly faster than the latter method.

Retrofitting Leakage Resilient Authenticated Encryption to Microcontrollers

The security of Internet of Things (IoT) devices relies on fundamental concepts such as cryptographically protected firmware updates. In this context attackers usually have physical access to a device and therefore side-channel attacks have to be considered. This makes the protection of required cryptographic keys and implementations challenging, especially for commercial off-the-shelf (COTS) microcontrollers that typically have no hardware countermeasures. In this work, we demonstrate how unprotected hardware AES engines of COTS microcontrollers can be efficiently protected against side-channel attacks by constructing a leakage resilient pseudo random function (LR-PRF). Using this side-channel protected building block, we implement a leakage resilient authenticated encryption with associated data (AEAD) scheme that enables secured firmware updates. We use concepts from leakage resilience to retrofit side-channel protection on unprotected hardware AES engines by means of software-only modifications. The LR-PRF construction leverages frequent key changes and low data complexity together with key dependent noise from parallel hardware to protect against side-channel attacks. Contrary to most other protection mechanisms such as time-based hiding, no additional true randomness is required. Our concept relies on parallel S-boxes in the AES hardware implementation, a feature that is fortunately present in many microcontrollers as a measure to increase performance. In a case study, we implement the protected AEAD scheme for two popular ARM Cortex-M microcontrollers with differing parallelism. We evaluate the protection capabilities in realistic IoT attack scenarios, where non-invasive EM probes or power consumption measurements are employed by the attacker. We show that the concept provides the side-channel hardening that is required for the long-term security of IoT devices.

Cryptanalysis of an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps

Recently, an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps (IEC-BPMC) was proposed, which includes two main parts: bit-level permutation for high 4-bit planes and bit-wise XOR diffusion. Some security analyses and experimental simulations were presented to support it to resist various attacks. However, it is found that the diffusion and permutation parts can be cracked separately by the divide-and-conquer strategy due to its inherent pitfalls. Then the equivalent diffusion key and the equivalent permutation key can be recovered by the chosen-plaintext attack method. Both theoretical analysis and experimental results demonstrate that IEC-BPMC is insecure against chosen-plaintext attack with low data complexity and computational complexity. Moreover, some other security defects of IEC-BPMC are revealed. Finally, some suggestions for improvement are given to enhance the security.

Modelling the utilization of cloud health information systems in the Iraqi public healthcare sector

The Iraqi healthcare sector has been suffering from health records management issues from the perspectives of low information technology integrity and data complexity. As a solution, cloud computing services can offer an alternative, low-cost, and reliable way to store, manage, and retrieve health-related data, as well as monitoring patients’ health conditions anywhere and anytime using any device with any platform. The migration to cloud services is not yet widespread in Iraqi health facilities due to various challenges, including security and privacy, legal policies, and implementation. For instance, there has been no research shedding light on the utilization of cloud computing services in Iraqi hospitals’ health information systems. This study proposed a model by defining the critical success factors influencing physicians’ confirmation and behavioral control toward utilizing cloud health information systems in Iraqi hospitals. The model’s variables were statistically investigated by utilizing an online questionnaire. Data were collected from a probability sample of 259 physicians working in four Iraqi high-IT hospitals. The collected ordinal data were analyzed using the PLS-SEM approach as a nonparametric second-generation multivariate analysis. The results showed that the effects of system compatibility, system complexity, security, and privacy on physicians’ confirmation and behavioral control were statistically significant. Both confirmation and behavioral control had a positive effect on physicians’ utilization of the technology in the Iraqi hospitals. It is believed that such finding may help to aid the current understanding of cloud health systems in managing health data as well as providing the necessary recommendations for policy makers to direct healthcare professionals to continuously consider the use of modern information and communications technology in the workplace.

Cryfa: a secure encryption tool for genomic data.

SummaryThe ever-increasing growth of high-throughput sequencing technologies has led to a great acceleration of medical and biological research and discovery. As these platforms advance, the amount of information for diverse genomes increases at unprecedented rates. Confidentiality, integrity and authenticity of such genomic information should be ensured due to its extremely sensitive nature. In this paper, we propose Cryfa, a fast secure encryption tool for genomic data, namely in Fasta, Fastq, VCF, SAM and BAM formats, which is also capable of reducing the storage size of Fasta and Fastq files. Cryfa uses advanced encryption standard (AES) encryption combined with a shuffling mechanism, which leads to a substantial enhancement of the security against low data complexity attacks. Compared to AES Crypt, a general-purpose encryption tool, Cryfa is an industry-oriented tool, which is able to provide confidentiality, integrity and authenticity of data at four times more speed; in addition, it can reduce the file sizes to 1/3. Due to the absence of a method similar to Cryfa, we have simulated its behavior with a combination of encryption and compression tools, for comparison purpose. For instance, our tool is nine times faster than its fastest competitor in Fasta files. Also, Cryfa has a very low memory usage (only a few megabytes), which makes it feasible to run on any computer.Availability and implementationSource codes and binaries are available, under GPLv3, at https://github.com/pratas/cryfa.Supplementary information Supplementary data are available at Bioinformatics online.

Subspace Trail Cryptanalysis and its Applications to AES

We introduce subspace trail cryptanalysis, a generalization of invariant subspace cryptanalysis. With this more generic treatment of subspaces we do no longer rely on specific choices of round constants or subkeys, and the resulting method is as such a potentially more powerful attack vector. Interestingly, subspace trail cryptanalysis in fact includes techniques based on impossible or truncated differentials and integrals as special cases. Choosing AES-128 as the perhaps most studied cipher, we describe distinguishers up to 5-round AES with a single unknown key. We report (and practically verify) competitive key-recovery attacks with very low data-complexity on 2, 3 and 4 rounds of AES. Additionally, we consider AES with a secret S-Box and we present a (generic) technique that allows to directly recover the secret key without finding any information about the secret S-Box. This approach allows to use e.g. truncated differential, impossible differential and integral attacks to find the secret key. Moreover, this technique works also for other AES-like constructions, if some very common conditions on the S-Box and on the MixColumns matrix (or its inverse) hold. As a consequence, such attacks allow to better highlight the security impact of linear mappings inside an AES-like block cipher. Finally, we show that our impossible differential attack on 5 rounds of AES with secret S-Box can be turned into a distinguisher for AES in the same setting as the one recently proposed by Sun, Liu, Guo, Qu and Rijmen at CRYPTO 2016

Food-Web and Ecosystem Structure of the Open-Ocean and Deep-Sea Environments of the Azores, NE Atlantic

The Marine Strategy Framework Directive intends to adopt ecosystem-based management for resources, biodiversity and habitats that puts emphasis on maintaining the health of the ecosystem alongside appropriate human use of the marine environment, for the benefit of current and future generations. Within the overall framework of ecosystem-based management, ecosystem models are tools to evaluate and gain insights in ecosystem properties. The low data availability and complexity of modelling deep-water ecosystems has limited the application of ecosystem models to few deep-water ecosystems. Here, we aim to develop an ecosystem model for the deep-sea and open ocean in the Azores exclusive economic zone with the overarching objective of characterising the food-web and ecosystem structure of the ecosystem. An ecosystem model with 45 functional groups, including a detritus group, two primary producer groups, eight invertebrate groups, 29 fish groups, three marine mammal groups, a turtle and a seabird group was built. Overall data quality measured by the pedigree index was estimated to be higher than the mean value of all published models. Therefore, the model was built with source data of an overall reasonable quality, especially considering the normally low data availability for deep-sea ecosystems. The total biomass (excluding detritus) of the modelled ecosystem for the whole area was calculated as 24.7 t km-². The mean trophic level for the total marine catch of the Azores was estimated to be 3.95, similar to the trophic level of the bathypelagic and medium-size pelagic fish. Trophic levels for the different functional groups were estimated to be similar to those obtained with stable isotopes and stomach contents analyses, with some exceptions on both ends of the trophic spectra. Omnivory indices were in general low, indicating prey speciation for the majority of the groups. Cephalopods, pelagic sharks and toothed whales were identified as groups with key ecological roles in the ecosystem. Due to concerns on the use of ecosystem models with low confidence in exploring management decisions and ecological theories, the current version of this model should only be use with caution until biomass estimates are validated with survey data or the model is fitted to time

First-order under-approximations of consistent query answers

Consistent Query Answering (CQA) is a principled approach for answering queries on inconsistent databases. The consistent answer to a query q on an inconsistent database db is the intersection of the answers to q on all repairs, where a repair is any consistent database that is maximally close to db. Unfortunately, computing consistent answers under primary key constraints has already exponential data complexity for very simple conjunctive queries, and is therefore completely impracticable.In this paper, we propose a new framework for divulging an inconsistent database to end users, which adopts two postulates. The first postulate complies with CQA and states that inconsistencies should never be divulged to end users. Therefore, end users should only get consistent query answers. The second postulate states that only those queries can be answered whose consistent answers can be obtained with low data complexity (i.e., by a polynomial-time algorithm or even a first-order logic query). User queries that exhibit a higher data complexity will be rejected.A significant problem in this framework is as follows: given a rejected query, find other queries, called under-approximations, that are accepted and whose consistent answers are contained in those of the rejected query. We provide solutions to this problem for the special case where the constraints are primary keys and the queries are self-join-free conjunctive queries.

Expressive Path Queries on Graph with Data

Graph data models have recently become popular owing to their applications, e.g., in social networks and the semantic web. Typical navigational query languages over graph databases - such as Conjunctive Regular Path Queries (CRPQs) - cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable to WL in terms of expressive power.